∫^(9) _(5)xsqrt(x^2+144)dx=(1/2) ∫^(9) _(5)sqrt(x^2+144)d(x^2+144)=
=(1/2) ∫^(9) _(5)(x^2+144)^(1/2)d(x^2+144)=
( табличный интеграл ∫ u^(α )du=u^(α +1)/(α +1);
u=x^2+144)
=(1/2)* (x^2+144)^((1/2)+1)/((1/2)+1) |^(9) _(5) =
=(1/3)sqrt(x^2+144)^3|^(9) _(5) =
=(1/3)*(sqrt(9^2+144)^3-sqrt(5^2+144)^3)=
=(1/3)sqrt(225^3)-(1/3)sqrt(169^3)=
=[b](1/3)*225*15-(1/3)*169*13= 1178/3[/b]